Question

Mathematically derive the 2nd law of motion​

Answer 1

Answer:

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Answer 2

$\Large{\bold{☣}}\;\red{\bf{Derive\; Newton\; Second\;Law\;Of\; Motion:-}}$

Statement:- The rate of change of momentum of a body is directly proportional to the net force acting on it and it takes place in the direction of net force.

Now, Consider a body of mass 'm' moving with a Velocity 'u'. Let an external force 'F' is acting on it in the same direction of the Velocity. And Let the velocity be changed to 'v' during a time period of '∆t'.

So, the momentum 'mu' changes to 'mv'.

Derivation of Formula:-

The Rate of change of momentum is ∆p/∆t

$→\;\Large{\bold{\frac{∆p}{∆t} = \frac{mv-mu}{∆t}}}$

$→\;\Large{\bold{\frac{m(v-u)}{∆t}}}$

• $\pink{\sf{a = \frac{v-u}{t}}}$

$→\;\Large{\bold{ma}}$

But, WKT

The Rate of Change of momentum is directly proportional to the force acting on it.

$→\;\Large{\bold{F\;∝\;\frac{∆p}{∆t}}}$

$→\;{\bold{F \;∝\;ma}}$

$→\;{\bold{F = Kma}}$

The unit of force is said such that, m = a = f = 1 unit.

So, 1 = k.1.1 → K = 1.

• K is constant of Proportionality, K = 1

$→\;\bold{F = 1(ma)}$

$→\;\sf{F = ma}$

Hence, Proved

• $\Large{\green{\bold{F = ma}}}$

$\boxed{\tt{@MrMonarque}}$

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